Kinsey is a very complex, poignant film that grows out of Liam Neeson's innocence and his close rapport with Laura Linney. Photograph: AP

In a simpler age, it's easy to believe that Liam Neeson's natural resources would have carried him to stardom. At 6ft4in, with that utterly honest gaze and a jaw like a shield, he would have been automatic casting as the hero in silent cinema based on honour and physical accomplishment. He had been raised in physical labour and boxing. Yet he was shy, noble and withdrawn from the macho code of boasting. A lot of women have fallen for him. Almost automatically, you assume he is a great star.

Yet, in truth, that's not the case. He is highly esteemed. In two ventures on Broadway, he got raves: with his wife Natasha Richardson in Anna Christie, and with Laura Linney in The Crucible. Yet here he comes, aged 55, in Seraphim Falls, a Canadian western directed by David van Ancker in which he plays a grim pursuer of Pierce Brosnan in Nevada in the 1860s. Neeson does his job well enough, though in truth he's more suited to being pursued than being the pursuer - witness his Valjean in Bille August's Les Miserables, where he was hounded by Geoffrey Rush.

On the other hand, there are things in Neeson's recent filmography that hardly seem credible - those utterly thankless parts in the later Star Wars pictures. And then he was killed off in the first half-hour of Gangs of New York while Daniel Day-Lewis had all the wicked fun. He was the Soviet commander of K-19: The Widowmaker, but that turned out a very lugubrious show in which the best you could say was that Neeson looked Russian. Neeson was as lost as anyone in Jan de Bont's dreadful remake of The Haunting. Can you place Before and After? It's a Barbet Schroeder film with Neeson and Meryl Streep as the parents of a child who has killed someone. Now, surely that ought to be memorable?

There really are only a few Neeson films that have worked. You'd have to include Rob Roy, his most emphatic athletic hero. But then you realise that the films in which Neeson has been at his best involve large men struggling to stay ordinary and filled with terrible doubts. It did not do much business, but Bill Condon's portrait of the pioneering sexual researcher Kinsey is a very complex, poignant film that grows out of Neeson's innocence and his close rapport with Laura Linney.

Still, Kinsey pales beside the quite extraordinary lead role in Steven Spielberg's Schindler's List. It may even be the case that the film would have felt flatter and cruder with a less subtle Schindler. For, as the film went on, so Oskar became increasingly daunted and stripped by circumstances he had first opposed as a gesture. It's very rare for American performances to grow in uncertainty, yet that is what Spielberg and Neeson accomplished. And we should never forget it.

I don't think Seraphim Falls is going to change the way we regard Neeson. But there's something on the horizon that could be momentous. We may not see it until 2009, but Neeson is Abraham Lincoln in a biopic based on the book by Doris Kearns Goodwin, and directed by Spielberg again. It's possible that America, emerging from the horrors of George W Bush's time in office, will be ready for a great presidential film. Lincoln was a man haunted by doubts. It might be something to remind us of what we have known, or nearly know now: that Liam Neeson can be a real star.